98 THE POPULAR SCIENCE MONTHLY. 



undoubtedly is — then every increase or diminution of this bundle is in 

 effect the formation of a new concept ; and Mill's objection that we 

 cannot think by means of concepts, because in reasoning we bring 

 before the mind a varying number of the attributes composing them, 

 is seen to be founded on the mistaken assumption that for every object 

 there is but'one corresponding concept, the truth being that an object 

 may be represented in thought by concepts without number. For 

 every object is the first link in innumerable chains of abstractions 

 varying in kind and diverging in direction with the comparisons insti- 

 tuted between it and other objects; and each of the links beyond the 

 first is a concept under which the object may, in scholastic phrase, be 

 subsumed. A horse, for example, may be considered mechanically 

 as a system of levers and strings, a self-regulating locomotive, a 

 machine, etc., or as a thousand pounds moving at the rate of 2.40 

 per mile, a heavy body, etc. ; or, chemically, as a congeries of cal- 

 cium and magnesium phosphates, carbonates, and fluorids, with albu- 

 mine, fibrine, and similar substances, as a compound of oxygen, hy- 

 drogen, carbon, nitrogen, sulphur, phosphorus, calcium, magnesium, 

 silicon, etc. ; or, zoologically, as a solipede, an ungulate, a mammal, an 

 animal, etc. ; or, economically, as a beast of burden, a domestic ani- 

 mal — and so on, indefinitely. The formation of concepts like these is 

 incident to all productive reasoning about individual things, and their 

 fixation by means of language (speaking of language in the compre- 

 hensive sense of all symbols by which forms of thought may be rep- 

 resented) an indispensable condition of the progress of scientific 

 knowledge, or, indeed, knowledge of any sort. 



On the other hand, the most obstinate conceptualist will not deny 

 that, before any one of these concepts can stand as the representative 

 of an actual, concrete object, it must be supplemented with all those 

 circumstances of singularity or particularity which were left behind in 

 the progress of abstraction. 



On closer examination, however, the war of words between Mill 

 and his antagonists proves to be a real contest of principles. The 

 elaboration of the data of experience into concepts implies an estab- 

 lishment of relations between these data in conformitv to laws not imme- 

 diately derivable from this experience itself — a mental digestion of the 

 crude material of sense ; and this is, in Mill's opinion, inadmissible in 

 view of the purely sensational origin of all knowledge. Mill has an 

 instinctive horror of every thing which purports to be something else 

 than a deliverance of sense, and contends that in our thought we are 

 at all times conversant, not with abstractions, but with facts. Whether 

 this be true or not, depends upon the meaning of the word " facts," 

 irrespective of the necessary reservation that all the facts about which 

 we know any thing at all are the facts of consciousness. A satisfac- 

 tory discussion of this topic (to which very valuable contributions 

 have been made by Mr. Ferrier) is beyond the scope of my inquiry; 



